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By C. E. Shoenfelt

Jan 1, 1942

By G. B. Kasik, George Sachs, George Espey

IT has been reported frequently that the hardness and strength vary over the cross section of cold-worked, particularly cold-drawn, material. Brass rod and wire usually have been found to possess a maximum strength and hardness near the surface.1,2 According to Sachs,' the center fiber has about the same strength as a wire stretched by the same amount in a tensile-test machine, the strength increasing toward the surface (Fig. I). These differences are particularly large for wire given a small reduction on drawing through a die with a wide opening. However, with increasing reduction and hardness, a tendency to form a thin soft surface skin becomes apparent. On the contrary, copper wire has usually been found to possess a soft surface skin3-5 and it has been reported by Harris3 that during the cold-drawing of hot-rolled wire the surface layer becomes increasingly softer than the core, while the layer of maximum strength moves toward the core, it being found near the surface at first. The increase of strength and hardness from the core to the skin is readily explained by the observation that, in addition to the stretching, the layers of a rod or wire are sheared more the closer they are to the surface.1,6-8 However, the presence of a soft surface layer can be attributed only to an annealing effect. The source of such a softening might be the extremely high temperature that originates from the friction between

Jan 1, 1942

By S. C. Oliphant, C. R. Houssiere, George H. Fancher

DRILLING mud can be an item of great expense on the Gulf Coast. In order to understand the nature of a drilling mud, it is desirable to know the composition and size of the mineral particles that are present, The supercentrifuge has been adapted to the fractionation of mud, and this paper discusses the calibration and methods of operation and control. An alignment chart has been prepared, which was found useful in this work. Typical data are included, showing the comparative reliability of the method.

Jan 1, 1942

MANY kinds of marcasite* are found since every metallic mineral, and perhaps some of the semiminerals, produces its own. I believe that [28v] rnarcasites are nothing other than the secondary materials and the menses of the conception of metals which, through insufficient time, have yet to arrive at their perfect age; and thus, because of

Jan 1, 1942

A GREAT labor, surely, is that of the coppersmith, since his every work must be hewn from the mass of copper by force of the hammer. At the beginning, middle, and, end all his works are inconvenient pieces and unpleasant to handle. If the work is done on the forge with the fire, it is done in order to refine or compose it into masses again, for drawing these out while hot with the blows of some heavy hammer, or in order to put the works in a condition that allows them to be drawn out while cold and worked. In this he puts all his labor and industry. He who works at this art often makes use of large hammers, sometimes of small ones, and sometimes of those that have a long iron head and a short handle. With these he is obliged ever to proceed in one of these activities, either extending the work lengthwise, narrowing it, or widening it. This is achieved by the manner and direction of striking and therefore it is sometimes hammered on the inside, sometimes on the outside, sometimes with the peen, and sometimes with the flat head. For instance, when he wishes to close it up he strikes it on the outside with the peen, and if he wishes to widen it he strikes it on the inside with either the flat head or the peen. In this way he proceeds to shape it with constant patience, and to make all the vessels that he works graceful. This metal, as I have told you, is soft, flexible, and tenacious under the hammer. It yields with a certain toughness, provided, however, that it is fine and without admixture of a trace of tin or other metal. That craftsman is a good master of this art who best makes every desired work

Jan 1, 1942

The following advertisements show the contemporary view of the value of coal on a tract, usually as compared with farming advantages of several kinds. Fayette Gazette and Union Advertiser, February 10, 1798: "For Sale in Washington twp., Fayette Co., 211 acres of land whereon is a good new grist merchant mill, a good stone dam, and a house for the miller, about two acres of bottom, cleared and fenced, an excellent coal bank and saw-mill seat unimproved." Pittsburgh Gazette, March 19 and 26, 1802: Ads. offering for sale two properties, one of 38 acres, "together with a Coal Pitt and Lime Quarry, lying on the Monongahela side of Grant's Hill, and within one mile and a half of Pittsburgh," and the other two tracts of 700 acres on "Racoon creek, contiguous to which is a valuable limestone quarry, and a quarry of building stone, also plenty of stone coal." Pittsburgh Gazette, Oct. 8, 1802: A farm between Pittsburgh and Greensburg "with house, barn and a Smith shop-also, a fine sugar camp, and a Coal Bank within sight of the house," was offered for sale. The Farmers Register, Greensburg, Pa., March 13, 1802: An advertisement of a "plantation, six miles from Greensburg, there are two coal banks on it, one at each end of the place." The Commonwealth, Pittsburgh, Aug. 4,1805: A number of lots were laid off on Saw Mill Run, nearly opposite the first opening made on the Pittsburgh seam. They were from two to twenty acres each "and a great quantity of Limestone and stone coal." Pittsburgh Gazette, Aug. 9, Sept. 6, Sept. 27, Oct. 4, 1811; The Commonwealth, Aug. 19, 1811: Five tracts were advertised that contained coal. One had "fine springs and an inexhaustible mine of coal;" one, "excellent sugar camps, coal banks and limestone and a good mill seat;" one, "good sugar camps, an excellent coal bank and an elegant seat for a distillery;" another, a tract of 45,000 acres in Allegheny and Butler Counties affording "stone coal and iron ore, and seats for water works;" and the last a tract on Beck's Run, four miles from Pittsburgh "and a coal pit opened about one fourth of a mile from the river." The Mercury, Pittsburgh, April 8, Jan. 14, Feb. 11, 1813; Pittsburgh Gazette, April 16, Dec. 3, 1813: These tracts were advertised during the year in the vicinity of the city. One had "a good sugar camp, woodland and plenty of coal;" another, "a sugar camp and a coal bank on the premises;" while the others were "well timbered or well watered and had excellent stone coal." The Mercury, Pittsburgh, Feb. 2, 1814: A farm was offered for sale on the headwaters of Robinson's Run, in Washington County, four miles from Burgettstown, containing 60 acres, "a young bearing orchard,... a coal bank and a good sugar camp." Genius of Liberty and Fayette Advertiser, Uniontown, Pa., March 2, 1814, carried an advertisement of a sale of lots in the new town of Perriopolis; "the quantity and quality of the clay, sand and salt licks, near the premises, together with the timber and abundance of .stone coals The town of Perriopolis was situated upon a . farm at one time belonging to Washington.

Jan 1, 1942

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Jan 1, 1942

By G. A. Vissac

In the presentation which follows, wash-ability curves, such as are commonly used in making studies preliminary to the cleaning of any coal or to the concentration of any mineral, have been reduced in each instance to a single straight line; thus all the most important characteristics of the coal or mineral are represented in a form more advantageous than that in which such data usually are shown. To obtain consistent results, float-and-sink data must be based on a single definite narrow size range, which may be designated "a coal unit." It will be shown that such units, each embodying a different size range, can be grouped to form what may be termed "a composite coal." A three-dimensional presentation will emerge, which will closely identify the coal, illustrate its characteristics in a new manner and explain many obscure facts. Float-and-sink Tests For the preliminary study of any cleaning or concentration problem, or in the control of any operation, float-and-sink tests must be made. The results of these tests are grouped in tabular form and then illustrated in various systems of curves; but if such a graphic representation is to have the utmost practical value, it must offer at least the following advantages: (I) It must be easier to read than the tabular results, and (2) it must be easy to plot, check and interpolate. The first requirement will be attained by reducing the number of curves to a minimum, and the second by some system of representation that will use only straight lines. Of the many washing curves now in use, only the "recovery curve," often known as the "composite curve"—a somewhat misleading term—will be considered; Any point on the recovery curve will show what percentage of weight of clean coal can be recovered when the mineral is washed at a certain specific gravity. As an example, the tests listed below Fig. I are illustrated in the drawing by a curve obtained by plotting (I) as abscissas the ash content of the coal recovered and (2) as ordinates the corresponding percentage of refuse discarded; but, in general practice, instead of writing down that weight, it is customary to set down its complement, which is the corresponding weight of coal recovered. From this curve can be deduced the information necessary for the solution of most practical problems. New Form of Graphic Presentation The resemblance of the recovery curve ill Fig. 1, or, for that matter, the recovery curve obtained in common practice! to a Power curve is apparent. The general equation of such a curve is Y = axn, where n is negative. Taking logarithms: log y = a + n log x. Using a logarithmic scale, the equation of the recovery curve will be Y = A + bX. On this logarithmic basis! the recovery graph will be a straight line, using the same variables as in Fig. I; namely, the ash con-

Jan 1, 1942

Washington has been the largest coal producing state of the Pacific Coast, and the only one producing coke commercially. With the exception of the few estimated figures, the tonnages in Table 71 are from Goodyear and other sources as shown. [ ]

Jan 1, 1942

By J. D. Sullivan, Chester R. Austin, J. L. Nunes

IT is characteristic of most shales and surface clays that a bloated or vesicular structure is produced by burning to a sufficiently high temperature, usually about 150° to 200°F. above the normal maturing temperature used when making common brick of the same material. Early investigators recognized this phenomenon and attributed it to the release or expansion of gases in the vitrified piece. A number of theories have been advanced on the source of the gas and the manner in which it is evolved, but none has been proved conclusively. T. E. Jackson's1 early theory that bloating was due to oxygen evolved by ferric oxide in forming ferrous oxide or ferrous silicate was never substantiated by experimental work. Orton2 thought this explanation unlikely, as all clays should bloat at the same temperature, if this were true. He found that clays bloated in the range from 1100° to I700°C. Also, many clays containing iron did not bloat at all, but fused. Orton also stated that oxidation of different types of carbon was a source of gas during burning of clay and should be expelled before vitrification was reached. Seger3 said that he had dissolved ferric oxide in glass with no apparent evolution of gas. Matson4 came to the conclusion that ferruginous clays burned to vitrification in an oxidizing atmosphere did not have the iron in a ferrous form. According to Wilson,5 the gases responsible for bloating might be entrapped air, water, sulphur dioxide, carbon monoxide, oxygen, and hydrocarbons. He spoke of two causes of bloating: (I) incomplete oxidation below the vitrification temperature, and (2) decomposition of compounds and evolution of gases above the vitrification temperature. Decomposition of calcium sulphate was given as the principal example of the latter. Bleininger and Montgomery6 stated that if any time after vitrification began the evolution of gaseous matter was rapid enough so that pressure was produced within the clay, bloating was certain to take place, and a vesicular structure would be formed. They recognized that initial structure, rate of heating, kiln atmosphere, and many other variables affected bloating. Work done by the Emergency Fleet Corporation7 indicated that clays suitable for bloating should be high in compounds of metallic oxides, carbon, sulphur, sodium, potassium, or other equivalent compounds, which either act as a flux or give off gas. Orton2 studied the chemical status of the carbon, iron, and sulphur in clays during various stages of burning, using a Huron shale that bloated under oxidizing or reducing conditions. He found that only a small amount of sulphur remained in the clay and that it could be detected only by dissolving the clay in hydrofluoric acid,i.e., the sulphur was in combination with the silica. Orton said that this sulphur was probably in the form of iron sulphide dissolved in the glass phase. The iron sulphide was not broken down by heating, but was dissolved in the basic slag or glass,

Jan 1, 1942

By R. F. Meel, J. K. Stanley

The recrystallization of cold-worked metals is studied ordinarily by determining the temperatures required for complete recrystallization to occur within a given arbitrary time period, usually within 15 min. to 2 hr. The results obtained are conventionally assembled in a three-dimensional diagram relating this temperature to the amount of cold-work (percentage deformation) and the resultant grain size, though sometimes other modes of representation are emp1oyed.l Such three-dimensional diagrams are not complete, for the number of variables exceeds the number represented. The process of recrystallization is characterized by a time-rate, a fact that is not portrayed upon ordinary recrystallization diagrams. It is known that recrystallization consists in the formation of new nuclei and the growth of these nuclei, a process that continues until the matrix is completely consumed and the original set of grains entirely replaced by the new. This knowledge is old.2 Truly heterogeneous reactions invariably proceed by nucleation and growth; the decomposition of eutectoid solid solutions provides an example about which much is known,3 and freezing, originally studied by Tammann, provides the classic example. Although recrystal- lization is not a heterogeneous reaction within the orthodox meaning of the term, the mechanism of the process is the same. As in eutectoid inversion and freezing, it should be possible to study the rate of isothermal recrystallization as a function of time, and it should also be possible to analyze the isothermal reaction curve into the component rates of nucleation and growth that determine them.* Other methods, not employing the rates of nucleation and growth, have been used to represent the rates of such reactions, but these in general have been artificial and have not led to progress. 4,5 The theory of recrystallization is not in advanced state; if recrystallization data were obtained in terms of the rate of isothermal recrystallization, and in terms of the rate of nucleation and the rate of growth of recrystallized grains, and in particular if the temperature coefficients of these rates were measured accurately, an adequate theory should be more readily developed.27 Such an effort requires proper experimental technique, but especially requires suitable methods of mathematical analysis to convert mcasurements made upon a surface of polish into values for the rate of nucleation and the rate of growth and to combine these into a rate of isothermal recrystallization. These methods are now available for the case of three-dimensional recrystallization (recrystallization of

Jan 1, 1942

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Jan 1, 1942

While the production of this state has not realized the early hopes that this coal would replace eastern coal on the Pacific Coast, it has been steady though small. Nearly all of the tonnages given are from Goodyear's, The Coal Mines of the Western Coast of the U. s., a carefully com- piled and accurate account of the development of the industry along the Pacific. [ ]

Jan 1, 1942

PAST AND PRESENT CHAIRMEN OF DIVISIONS Institute of Metals Iron and Steel Mineral Industry Industrial Minerals Year Division Petroleum Division Division Coal Division Education Division Division 1918 W. M. CORSET 1919 " 1920 W. H. BASSETT 1921 " 1922 W. B. PRICE RALPH ARNOLD 1923 E. DEGOLYER 1924 G. B. ELLIOTT 1925 F. JULIUS FOHS 1926 P. D. MERICA 1927 11 JOHN. M. LOVEJOY 1928 S. SKOWRONSKI A. W. AMBROSE RALPH H. SWEETSER ' 1929 " J. B. UMPLEHY G. B. WATERHOUSE 1930 ZAY JEFFRIES C. V. MILLIKAN W. J. MACKENZIE HOWARD N. EAVENSON 1931 SAM TOUR C. E. BEECHER F. M. BECKET 1932 C. H. MATHEWSON EARL OLIVER F. N. SPELLER THOMAS G. FEAR C. H. FULTON 1933 T. S. FULLER W. E. WRATHER JOHN JOHNSTON ELI T. CONNOR " 1934 J. L. CHRISTIE H. D. WILDE, JR. L. F. REINARTZ " T. T. READ 1935 W. M. PEIRCE HARRY H. POWER A. B. KINZEL JOHN T. RYAN SAMUEL H. DOLBEAR 1936 E. H. DIX, JR. HALLAN N. MARSH C. E. WILLIAMS EUGENE MCAULIFFE WILLIAM B. PLANK OLIVER BOWLES 1937 A. J. PHILLIPS M. ALBERTSON FRANCIS B. FOLEY J. B. MORROW " CHESTER A. FULTON 1938 R. F. MEHL G. B. CORLESS J. T. MACKENZIE PAUL WEIR FRANCIS A.THOMSON J. R. THOENEN 1939 R. H. LEACH W. H. GETS J. HUNTER NEAD C. A. GIBBONS " M. M. LEIGHTON 1940 E. M. Wise T. V. MOORE F. T. SISCO C. E. LA WALL W. R. CHEDSEY W. M. WEIGEL 1941 D. K. CRAMPTON E. A. STEPHENSON C. H. HERTY, JR. JULIAN E. TOBEY " PAUL M. TYLER 1942 CARL E. SWARTZ HARRY P. STOLZ E. C. SMITH NEWELL G. ALFORD A. F. GREAVES-WALKER B. L. MILLER

Jan 1, 1942

By H. M. Morse

Mississippi, during the year 1941, experienced the greatest diversity of oil activity since the beginning of oil interest in the state—core tests for exploration, core tests for sulphur, continued drilling at Tinsley for production, and wildcatting, which brought to light two new oil fields and two new salt domes. There were 45 wildcat wells drilled in 1941, which showed greater results and findings geologically than the 85 drilled in 1940. Tinsley Oil Field (Yazoo County).—The Tinsley oil field, with its boundaries fairly well defined now, is 8 miles long and 3 miles wide at its widest point. During the past year 213 producing wells were completed, which brought the total number of producers in the field by the end of 1941 to 325 wells. Seven producing sands have been logged, with a total average thickness of 30 ft. of oil sand. The producing formations are the Selma, Eutaw and Tuscaloosa. The average total depth of the wells is 5012 ft. The average gravity of the oil is 35.4°. Production for 1941 was approximately 15,500,000 bbl. of oil. Vaughan-Pickens Oil Field (Yazoo County).—At the end of 1941 only three wells were Producing in this field, the fourth having been abandoned. The total production for the field for the year was approximately 250,000 bbl. of oil. The producing sand is the Wilburn, in the Eutaw formation. Cary Field (Sharkey County).—The British American Oil Producing Co. completed, on Sept. I, 1941, its F. B. Houston No. A-I well, sec. 23, T. 11 N., R. 7 W. It is

Jan 1, 1942

By Max Y. Seaton

THE scope of this paper will be limited to finished materials that contain a large preponderance (around 80 per cent or more) of magnesium oxide. The large and commercially important production of refractory dolomite and modified dolomites is not discussed here, and the production of magnesium basic carbonate for use as a heat insulator is barely mentioned. The discussion is confined mainly to magnesias produced in comparatively great quantity by direct processing of naturally occurring raw materials and hence excludes secondary or highly purified products such as pharmaceutical products or U.S.P. light and heavy calcined magnesias of commerce. NOMENCLATURE The nomenclature of the magnesia products that will be discussed is somewhat confusing, in that it is customary in the trade to designate as "calcined magnesite" the materials that result from the calcining of magnesite to temperatures that remove the contained carbon dioxide. The finished product, therefore, is not magnesite at all but simply a more or less pure magnesium oxide or magnesia. Furthermore, partly for statistical and partly for commercial reasons, it has been customary, during recent years, to classify as "calcined magnesite" products that result from the heat-treatment of magnesium hydroxide precipitated from magnesium-containing brines; products that, obviously, have no relationship whatever to magnesite. In the listing of magnesia-containing materials, tonnages of which are regularly reported by the Bureau of Mines, reports ordinarily are made under two headings: "caustic calcined" magnesite, in which all of the varieties of products treated at relatively low temperatures are lumped; and "dead-burned" magnesite, in which are included both high-purity and low-purity, and particularly both high-iron and low-iron, materials that have been so heat-treated that the magnesium oxide occurs predominantly as crystalline periclase-materials used almost entirely for refractory purposes. In 1940 the apparent domestic consumption of "caustic calcined" magnesite was approximately 17,000 tons, about 95 per cent of which was produced in this country. The apparent consumption of "dead-burned" magnesite was approximately 172,000 tons, some 82 per cent of which was domestically produced. In both total quantity and percentage of material produced within the United States, these figures are record highs for many years past. UTILIZATION As indicated by these figures, the major tonnage outlet for magnesia is the refractories industry, in which magnesia is employed principally in three ways: (I) as dead-burned grain magnesite for the construction and maintenance of the hearths or bottoms of basic open-hearth furnaces; (2) in the form of refractory magnesite bricks and shapes; and (3) as a chemical

Jan 1, 1942

SINCE I have mentioned the art of alchemy in. many parts of this treatise of mine, especially when 'came to the description of the practice of various operations,* I do not here intend to argue as to whether it may be called true or not. But in case it is true, inasmuch as it is seen in operation to be a result dependent on the actions and virtues of fires, I should not pass by in silence without speaking at all of this art here, nor would I wish to do so, especially since I think that you do not really know what it is except in so far as common report is heard everywhere to the effect that whoever carries it to completion makes silver and gold with it. Because of this belief, many seek it with much time, labor, and expense, as I know you have often heard related, if not elsewhere, by me in the chapter on gold that I have written in this volume. Now do not think that I wish to teach you this art here, for I am one of those who do not know it. Therefore I shall tell you here, so that you may know more, only. that those workers who so eagerly follow after and seek it proceed by just two pathways. One is that which takes its enlightenment from the words of the wise philosophers, by means of which they think to attain it. This they call the just, holy, and good way, and they, say that in this they are but imitators and assistants of Nature, indeed, manipulators and true physicians-of .mineral bodies, purging them of superfluities and assisting them by augmenting their virtue and freeing them from their defects. In this way they sometimes proceed to corrupt these bodies in order to be able to separate the elements they contain so as to reduce them, if possible, to their primary materials, as they call them, or sometimes they convert them into new substances by means of this art or by adding another spirit different from the first one. Thus they seek in this way to bring these materials to a certain point of corruption or to a separation of elements, or to remove or add spirits to things, or to make coarse materials subtle and sometimes to make subtle materials coarse. Therefore, as you can understand, these persons, with bridle broken, run a circular track night and day, without ever having rest; and surely I do not know whether anyone has ever arrived at the desired goal. Nevertheless, even though the goal of this art were emptiness, as many

Jan 1, 1942

By Walter R. Hibbard, Cyril Stanley Smith

IN 1929 one of the authors' determined the constitution of copper-silicon-manganese alloys containing over 90 per cent copper. Through a combination of circumstances the presence of the copper-silicon kappa phase was overlooked in both binary and ternary systems. In the binary system the omission has already been rectified.2,3 To establish the limits of this phase in the ternary system, the samples that had been heat-treated at the time of the original research have now been re-examined, using more careful technique. Full details of the compositions used and the temperatures and times of heat-treatment are to be found in the earlier paper .2 The etching reagent now used to distinguish the kappa phase had the following composition: hydrogen peroxide (30 vol.), 20 c.c.; water, 25 c.c.; 20 per cent potassium hydroxide solution, 5 c.c.; ammonium hydroxide (0.90 sp. gr.), 50 c.c. Table I lists the newly observed structures. In virtually every case the constituents are the same as those previously recorded, except where kappa is now shown to be present as a result of the improved etching technique. A few other changes will be noted (No. 138 at 450°C., No. 149 at 550°C., Nos. 153 and 149 at 750°C.). The change from liquid to beta in equilibrium with kappa in No. 139 at 800°C. is based upon newly heat-treated samples. The alloy is very near the solidus at 800°C. and probably there was a slight error in the old heat-treatment temperature. The isothermal phase diagrams shown in Figs. 1 to 6 were reconstructed on the basis of the new studies. The presence of manganese does not greatly change the composition limits of the kappa phase or cause the [K = a + ?] change to occur at a markedly different temperature. There is some uncertainty regarding the range of existence of beta, for alloys were not spaced very closely in composition. The proposed diagrams, however, are in accordance with the available experimental data and with the dictates of the phase rule. Theoretically necessary fields with no experimental points are delineated by dotted lines. The alpha boundaries at all temperatures are shown together in Fig. 7. This includes also some additional points on the alpha boundary at 300° and 350°C., which were obtained as a result of electrical-conductivity measurements. Two series of seven alloys with increasing manganese content but with silicon constant at 1.90 ± 0.03 per cent or 2.42 ± 0.05 per cent were cast in ingots of 3-in, diameter. These were hot-rolled, homogenized and drawn to wire, finished at 0.08-in. diameter with a 61 per cent reduction of area following annealing at 900°C. Conductivity determinations were made before and after annealing for 30 days at 300°C. or 21 days at 350°C. Figs. 8 and 9 show the change of conductivity produced by this annealing, plotted against manganese

Jan 1, 1942

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Jan 1, 1942

By Raymond Mancha

When calculating the pressure-volume characteristics of projected mine-ventilating circuits by orthodox methods, certain basic assumptions are required in order to employ the various available empirical data. It is assumed, for example, that the mine air is an incompressible fluid subjected to isothermal flow, an assumption sufficiently accurate for practical purposes since pressure and temperature differentials are small throughout the average circuit. A more erroneous assumption, however, is that all air is accounted for as it travels throughout the mine. No attempt is usually made to evaluate stopping leakage as it occurs; instead, the air volume required at the last crosscuts is assumed to enter the mine, travel the various intake air courses intact, sweep the workings and travel out by the return air courses to the point or points of exit from the mine. Actually, there is a leakage of air from intake to return at every stopping, the quantity of this leakage depending upon the tightness of the stopping and the pressure difference across the stopping. Unfortunately, a lack of empirical data and knowledge of the condition of individual stoppings makes an exact analysis of underground stopping leakage impossible. Generally, leakage is most severe through the old stoppings outbye the circuit. These are also subjected to higher pressure differences than the newer inbye stoppings. Therefore the circuit air volume diminishes at a decreasing rate progressing from outbye to inbye the circuit. Consider a simple mine circuit consisting of one intake and one return air course, each of equal and uniform section area and interconnected at regular intervals with crosscuts equipped with stoppings. At any point X inbye the circuit the air volume q on the intake air course equals that on the return air course and decreases with diminishing rate from outbye to inbye the circuit between the limits of Q1 completely outbye and Q completely inbye. Such a volume change is represented by curve a, Fig. I, which is computed with the aid of the equation q = Q1- (Q1- Q)(X + L)N. This equation results from the general algebraic equation of form q = k, — kXN after solving for kl and k with the knowledge that completely outbye X = o and q = QL, also completely inbye X = L and q = Q. Curves a, b and c, Fig. I, show values of q as ordinates versus values of X as abscissas, for values of N equal to 0.50, 1.00 and 2.00, respectively. Distribution of underground stopping 1eakage directly affects the air-volume distribution along the circuit, which in turn determines the circuit pressure gradient. To deliver any required air volume inbye a circuit or portion thereof requires a higher circuit-pressure differential if stoppings leak than is necessary with tight stoppings. Every mining engineer engaged in the analysis of projected mine-ventilation circuits is therefore confronted with the problem of making proper allowance for the effects of leaking stoppings. The purpose of this paper is to present evidence in support of the author's suggestion that circuit pressure increase (per cent)

Jan 1, 1942